In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

   Receipt date:10/27/2021    accepted date:12/15/2021     Publication date:31/12/2021

        This work is licensed under a Creative Commons Attribution 4.0 International License.

The phenomenon of extremist extremism (terrorism) was one of the most prominent issues that took a large space in the twenty-first century, in which cognitive motives were mixed with strategic and ideological motives, leading to the emergence of terrorist extremi

The aims of research is to identify the role of strategic human resource management Practices in organizational performance improvement in the Baghdad soft drinks company, as well as the implications of the results for both managers and practitioners.

In order to achieve the objectives of the research, the researcher designed questionnaire included (40) items to collect the initial data from the research sample consisting of (53) Single. In light of that has been collecting and analyzing data and test hypotheses using the statistical package for Social Sciences (SPSS21), and use a number of statistical methods to achieve the goal of the research, including the means, standard deviations and simple correla

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            Irak’ın osmanlıcada yazılan sayısız elyazmalar çeşitli illerinde bulunur. Bunlardan Irak’ın başkenti olan Bağdat’tır. Irak Ulusal Müzesi Bağdad’ın uygarlık yerlerindendir. Elyazması Evi müzenin en önemli bölümleri sayılır. Orada osmanlıcada yazılan çok değerli elyazmalar bulunur. Bu elyazmalarından  birisini ( fotokopi ) elde edip üzerinde çalışılmaktadır. Eser Antoloji  şeklinde yazılmış. Bu eserden Sadullah Pâşâ’nın On Dokuzuncu Asır Manzumesini seçip ele alınmaktadır.

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         لقد نشا علم التحقيق على ايدي المحدثين المسلمين الذين  وضعوا قواعد هذا  العلم  وظهرت مؤلفات  عدة في هذا المجال ، لكن ما قام به الاقدمون لم يشكل قواعد علم مستقل  بذاته ومنذ ظهور الطباعة بدأت حركة تحقيق المخطوطات ، وتعددت  مناهج التحقيق فكان للمستشرقين منهجهم الخاص وظهر منهج التحقيق والاخراج الفني والعلمي للمخطوط .

This study was concerned with using ozone gas in drinking water treatment plant at Ibn-Sina Company. The main purpose of this research is to find the best contactor for ozone unit proposed. An investigation was conducted to study the absorption of ozone by water in two type of absorber. The effects of the process variables (such as height of water column, contact time, and pH) on the amount of ozone absorbed were investigated. Box-Wilson central composite rotatable design is used to design the experimental work for the mentioned variables. It was found that the optimum value of the variables studied was:
i) Height of water column (90 cm)
ii) Contact time (17-18 min)
iii) PH (7 - 7.5)

Specialized hardware implementations of Artificial Neural Networks (ANNs) can offer faster execution than general-purpose microprocessors by taking advantage of reusable modules, parallel processes and specialized computational components. Modern high-density Field Programmable Gate Arrays (FPGAs) offer the required flexibility and fast design-to-implementation time with the possibility of exploiting highly parallel computations like those required by ANNs in hardware. The bounded width of the data in FPGA ANNs will add an additional error to the result of the output. This paper derives the equations of the additional error value that generate from bounded width of the data and proposed a method to reduce the effect of the error to give

If we go beyond the technical aspects of the Web 2.0, and we focus specifically on its interactive characteristics, we may say it represents not only a fundamental shift in the structure of the press institutions and its practices but also a shift in the relationships that existed, previously, between the press and the audience. Web 2.0 has enabled the newspapers to renovate their representations and practices of the profession and opens to the new horizons either in terms of readership or advertising revenues. Parallel to that it also has empowered the user to transcend the passivity he has always been confined in and has become a more active participant in the creation and generation of media contents even though this practice is somew